Analyzing fuzzy boundary value problems: a study on the influence of mitochondria and ER fluxes on calcium ions in neuron cells

Abu-Arqub O, El-Ajou A, Momani S, Shawagfeh N (2013) Analytical solutions of fuzzy initial value problems by HAM. Appl Math Inf Sci 7:1903–1919. https://doi.org/10.12785/amis/070528

Article  Google Scholar 

Alsharo DM, Jameel AF, Alomari AK et al (2019) New semi-analytical method for solving two point nth order fuzzy boundary value problem. Int J Math Model Numer Optim 9:12. https://doi.org/10.1504/IJMMNO.2019.10017923

Article  Google Scholar 

Arancio O et al (2017) Calcium hypothesis of Alzheimer’s disease and brain aging: a framework for integrating new evidence into a comprehensive theory of pathogenesis. Alzheimers Dement 13:178-182.e17. https://doi.org/10.1016/j.jalz.2016.12.006

Article  Google Scholar 

Bailey PB, Shampine LF (1969) Existence from uniqueness for two point boundary value problems. J Math Anal Appl 25(3):569–574. https://doi.org/10.1016/0022-247X(69)90256-X

Article  Google Scholar 

Bede B (2006) A note on “two-point boundary value problems associated with non-linear fuzzy differential equations.” Fuzzy Sets Syst 157:986–989. https://doi.org/10.1016/j.fss.2005.09.006

Article  Google Scholar 

Bede B, Stefanini L (2011) Solution of fuzzy differential equations with generalized differentiability using LU-parametric representation. In: Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-2011). Atlantis Press, Paris, France: https://doi.org/10.2991/eusflat.2011.106

Bede B, Stefanini L (2013) Generalized differentiability of fuzzy-valued functions. Fuzzy Sets Syst 230:119–141. https://doi.org/10.1016/j.fss.2012.10.003

Article  Google Scholar 

Bellotti R, Pascazio S (2012) Editorial: advanced physical methods in brain research. Eur Phys J Plus 127:145. https://doi.org/10.1140/epjp/i2012-12145-4

Article  Google Scholar 

Berridge MJ (2013) Dysregulation of neural calcium signaling in Alzheimer disease, bipolar disorder and schizophrenia. Prion 7(1):2–13. https://doi.org/10.4161/pri.21767

Article  CAS  PubMed  PubMed Central  Google Scholar 

Bertram R, Gram Pedersen M, Luciani DS, Sherman A (2006) A simplified model for mitochondrial ATP production. J Theor Biol 243:575–586. https://doi.org/10.1016/j.jtbi.2006.07.019

Article  CAS  PubMed  Google Scholar 

Black C, Black C (2005) Student solutions manual to accompany Elementary linear algebra with applications, 9th ed. Wiley

Bojarski L, Herms J, Kuznicki J (2008) Calcium dysregulation in Alzheimer’s disease. Neurochem Int 52:621–633. https://doi.org/10.1016/j.neuint.2007.10.002

Article  CAS  PubMed  Google Scholar 

Brawek B, Garaschuk O (2014) Network-wide dysregulation of calcium homeostasis in Alzheimer’s disease. Cell Tissue Res 357:427–438. https://doi.org/10.1007/s00441-014-1798-8

Article  CAS  PubMed  Google Scholar 

Buckley JJ, Eslami E, Feuring T (2002) Fuzzy differential equations. In: Part of the studies in fuzziness and soft computing book series STUDFUZZ, Chapter 7, vol. 91. pp 145–163

Buckley JJ, Feuring T (2001) Fuzzy initial value problem for th-order linear differential equations. Fuzzy Sets Syst 121:247–255. https://doi.org/10.1016/S0165-0114(00)00028-2

Article  Google Scholar 

Dave DD, Jha BK (2018) Analytically depicting the calcium diffusion for Alzheimer’s affected cell. Int J Biomathema 11(7):1850088. https://doi.org/10.1142/S1793524518500882

Dave DD, Jha BK (2020) 3D mathematical modeling of calcium signaling in Alzheimer’s disease. Netw Model Anal Health Inform Bioinforma 9:1. https://doi.org/10.1007/s13721-019-0207-3

Article  Google Scholar 

Dave DD, Jha BK (2021) Mathematical modeling of calcium oscillatory patterns in a neuron. Interdiscip Sci 13:12–24. https://doi.org/10.1007/s12539-020-00401-8

Article  CAS  PubMed  Google Scholar 

Dave DD, Jha BK (2023) Finite element technique to explicate calcium diffusion in Alzheimer’s disease, 1st edn. In: Computational and analytic methods in biological sciences. River Publisher, pp 22

De Young GW, Keizer J (1992) A single-pool inositol 1,4,5-trisphosphate-receptor-based model for agonist-stimulated oscillations in Ca2+ concentration. Proc Natl Acad Sci 89:9895–9899. https://doi.org/10.1073/pnas.89.20.9895

Article  PubMed  PubMed Central  Google Scholar 

Gasilov NA, Amrahov SE, Fatullayev AG (2011) A geometric approach to solve fuzzy linear systems of differential equations. Appl Math Inf Sci 5:484–495

Google Scholar 

Gasilov NA, Hashimoglu IF, Amrahov SE, Fatullayev AG (2012) A new approach to non-homogeneous fuzzy initial value problem. Comput Model Eng Sci (CMES) 85(4):367–378

Google Scholar 

Gasilov N, Amrahov ŞE, Fatullayev AG (2014) Solution of linear differential equations with fuzzy boundary values. Fuzzy Sets Syst 257:169–183. https://doi.org/10.1016/j.fss.2013.08.008

Article  Google Scholar 

Goetschel R, Voxman W (1986) Elementary fuzzy calculus. Fuzzy Sets Syst 18:31–43. https://doi.org/10.1016/0165-0114(86)90026-6

Article  Google Scholar 

Hüllermeier E (1997) An approach to modelling and simulation of uncertain dynamical systems. Int J Unc Fuzz Knowl Based Syst 05:117–137. https://doi.org/10.1142/S0218488597000117

Article  Google Scholar 

Jameel AF, Shather AH, Anakira NR et al (2020) Comparison for the approximate solution of the second-order fuzzy nonlinear differential equation with fuzzy initial conditions. Math Stat 8:527–534. https://doi.org/10.13189/ms.2020.080505

Article  Google Scholar 

Jha A, Adlakha N (2014) Finite element model to study the effect of exogenous buffer on calcium dynamics in dendritic spines. Int J Model Simul Sci Comput 5(2):1350027. https://doi.org/10.1142/S179396231350027X

Jha N, Kritika (2023) Approximate analytic solution for tumour growth and human head heat distribution singular boundary value model by high-resolution order-preserving fuzzy transform: eBook ISBN9781003393238

Jha BK, Adlakha N, Mehta MN (2012) Finite element model to study calcium diffusion in astrocytes. Int J Pure Appl Math 78: ISSN: 1311–8080

Jha BK, Adlakha N, Mehta MN (2013) Two-dimensional finite element model to study calcium distribution in astrocytes in presence of VGCC and excess buffer. Int J Model Simul Sci Comput 4(2):1250030. https://doi.org/10.1142/S1793962312500304

Jha BK, Adlakha N, Mehta MN (2014) Two-dimensional finite element model to study calcium distribution in astrocytes in presence of excess buffer. Int J Biomathema 7(3):1450031. https://doi.org/10.1142/S1793524514500314

Jha BK, Joshi H, Dave DD (2018) Portraying the effect of calcium-binding proteins on cytosolic calcium concentration distribution fractionally in nerve cells. Interdiscip Sci 10:674–685. https://doi.org/10.1007/s12539-016-0202-7

Article  CAS  PubMed  Google Scholar 

Joshi H, Jha BK (2020) Fractional-order mathematical model for calcium distribution in nerve cells. Comput Appl Math 39:56. https://doi.org/10.1007/s40314-020-1082-3

Article  Google Scholar 

Joshi H, Jha BK (2022) 2D dynamic analysis of the disturbances in the calcium neuronal model and its implications in neurodegenerative disease. Cogn Neurodyn. https://doi.org/10.1007/s11571-022-09903-1

Article  PubMed  Google Scholar 

Joshi H, Jha BK, Dave DD (2018) Mathematical model to study the effect of mitochondria on Ca2+ diffusion in Parkinsonic nerve cells. In: AIP Conference Proceedings, vol. 1975. AIP Publishing. https://doi.org/10.1063/1.5042183

Kaleva O (1987) Fuzzy differential equations. Fuzzy Sets Syst 24:301–317. https://doi.org/10.1016/0165-0114(87)90029-7

Article  Google Scholar 

Kaleva O (1990) The cauchy problem for fuzzy differential equations. Fuzzy Sets Syst 35:389–396. https://doi.org/10.1016/0165-0114(90)90010-4

Article  Google Scholar 

Keener J, Sneyd J (eds) (2009) Mathematical Physiology. Springer, New York

Google Scholar 

Khastan A, Nieto JJ (2010) A boundary value problem for second order fuzzy differential equations. Nonlinear Anal Theory Methods Appl 72:3583–3593. https://doi.org/10.1016/j.na.2009.12.038

Article  Google Scholar 

Kothiya A, Adlakha N (2023) Simulation of biochemical dynamics of Ca2+ and  PLC in fibroblast cell. J Bioenerg Biomembr 55:267–287. https://doi.org/10.1007/s10863-023-09976-5

Article  CAS  PubMed  Google Scholar 

L. Glass JDM, R. V. Kohn, SS Sastry PSK (2002) Interdisciplinary Applied Mathematics, Third. Springer, New York Berlin Heidelberg

LaFerla FM (2002) Calcium dyshomeostasis and intracellular signalling in alzheimer’s disease. Nat Rev Neurosci 3:862–872. https://doi.org/10.1038/nrn960

Article  CAS  PubMed  Google Scholar 

Liao S (2005) Comparison between the homotopy analysis method and homotopy perturbation method. Appl Math Comput 169:1186–1194. https://doi.org/10.1016/j.amc.2004.10.058

Article  Google Scholar 

Liao S (2006) Series solutions of unsteady boundary-layer flows over a stretching flat plate. Stud Appl Math 117:239–263. https://doi.org/10.1111/j.1467-9590.2006.00354.x

Article  Google Scholar 

Liao Y, Dong Y, Cheng J (2017) The function of the mitochondrial calcium uniporter in neurodegenerative disorders. Int J Mol Sci 18(2):248. https://doi.org/10.3390/ijms18020248

Article  CAS  PubMed  PubMed Central  Google Scholar 

Magi S, Castaldo P, MacRi ML et al (2016) Intracellular calcium dysregulation: implications for Alzheimer’s disease. Biomed Res Int 14. https://doi.org/10.1155/2016/6701324

Manhas N, Pardasani KR (2014) Mathematical model to study IP3 dynamics dependent calcium oscillations in pancreatic acinar cells. J Med Imaging Health Inform 4(6):874–880. https://doi.org/10.1166/jmihi.2014.1333

Article  Google Scholar 

Mishra V, Adlakha N (2023) Spatio temporal interdependent calcium and buffer dynamics regulating DAG in a hepatocyte cell due to obesity. J Bioenerg Biomembr 55:249–266. https://doi.org/10.1007/s10863-023-09973-8

Article  CAS  PubMed  Google Scholar 

Muzzioli S, Reynaerts H (2006) Fuzzy linear systems of the form A1x + b1 = A 2x + b2. Fuzzy Sets Syst 157:939–951. https://doi.org/10.1016/j.fss.2005.09.005

Article  Google Scholar 

Naik PA, Pardasani KR (2019) Three-dimensional finite element model to study effect of RyR calcium channel, ER leak and SERCA pump on calcium distribution in Oocyte Cell. Int J Comput Methods 16:1850091. https://doi.org/10.1142/S0219876218500913

Article  Google Scholar 

Nieto JJ, Rodríguez-López R, Villanueva-Pesqueira M (2011) Exact solution to the periodic boundary value problem for a first-order linear fuzzy differential equation with impulses. Fuzzy Optim Decis Making 10:323–339. https://doi.org/10.1007/s10700-011-9108-3

Article  Google Scholar 

O’Regan D, Lakshmikantham V, Nieto JJ (2003) Initial and boundary value problems for fuzzy differential equations. Nonlinear Anal Theory Methods Appl 54:405–415. https://doi.org/10.1016/S0362-546X(03)00097-X

Article  Google Scholar 

Pathak K, Adlakha N (2016) Finite element model to study two dimensional unsteady state calcium distribution in cardiac myocytes. Alexandria J Med 52:261–268. https://doi.org/10.1016/j.ajme.2015.09.007

Comments (0)

No login
gif